The Ground Level Enhancement (GLE), discovered back in 1942, is a phenomenon in which there is a sharp increase of the counting rate in neutron monitors over a short period of time. These events are very rare (76 recorded yet), which complicates their detailed study and understanding of the processes of their production. To date, there are several hypotheses aimed to explain the physics behind GLE, but none of them has been definitively confirmed. The main task facing the researchers is to determine the cause of these short-term but intense increases recorded by neutron monitors. This study proposes a new approach to the analysis of recorded GLE events. The paper focuses on the analysis of the counting rate increases in neutron monitors themselves trying to identify their characteristic features that may indicate a different nature of the origin of these events. The study also considers the problem of the determination of the criteria for events to be classified as GLE.